Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Covariance tracking via geometric particle filtering
EURASIP Journal on Advances in Signal Processing - Special issue on advanced image processing for defense and security applications
Computer Vision and Image Understanding
Statistics of shape via principal geodesic analysis on lie groups
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Applied Stochastic Models in Business and Industry
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Monte Carlo (MC) methods have become an important tool for inferences in non-Gaussian and non-Euclidean settings. We study their use in those signal/image processing scenarios where the parameter spaces are certain Riemannian manifolds (finite-dimensional Lie groups and their quotient sets). We investigate the estimation of means and variances of the manifold-valued parameters, using two popular sampling methods: independent and importance sampling. Using Euclidean embeddings, we specify a notion of extrinsic means, employ Monte Carlo methods to estimate these means, and utilize large-sample asymptotics to approximate the estimator covariances. Experimental results are presented for target pose estimation (orthogonal groups) and signal subspace estimation (Grassmann manifolds). Asymptotic covariances are utilized to construct confidence regions, to compare estimators, and to determine the sample size for MC sampling